Identify the vertical asymptotes of f (x) = x-4 over x2+13x+36

A) x = - 9 and x = - 4

B) x = - 9 and x=4

C) x=9 and x=-4

D) x=9 and x=4

Given:

f (x) = (x-4) / (x² + 13x + 36)

The vertical asymptotes of f (x) occur when the denominator is zero because f (x) becomes undefined.

Note that

x² + 13x + 36 = (x + 4) (x + 9).

Therefore

f (x) = (x - 4) / [ (x + 4) (x + 9) ]

The denominator is zero, when

(a) x + 4 = 0 = > x = - 4, or

(b) x + 9 = 0 = > x = - 9.

Therefore the function becomes undefined a x = - 4, or x = - 9, where the vertical asymptotes occur.

Answer: A) x = - 9 and x = - 4.